# Speed of Water Coming out of Vertical Cylinder

1. Jan 8, 2014

### slasakai

1. The problem statement, all variables and given/known data
A vertical cylinder with diameter 9 cm has an outlet on its side with diameter 3cm, water is filled to height 50cm and the outlet is 5 cm above the bottom of the cylinder. the outlet is closed by a valve, calculate the force required to stop the cylinder from moving when the valve is opened.

2. Relevant equations
A1V1=A2V2
Bernoulli's Equation [too long to type!]

3. The attempt at a solution

I'm struggling as no pressures are provided, and applying Bernoulli's equation isn't straightforward. I'm not sure whether it's possible to interpret it as the fact that the top of the cylinder is open, as this would make the problem simpler. I would really appreciate some insight to this question :)

2. Jan 8, 2014

### Travis_King

How do you find pressure of a liquid at a given depth? (or rather, when the surface of the water is a certain height above where you're desired measurement point)

3. Jan 8, 2014

### SteamKing

Staff Emeritus
You have water in the cylinder. You are given the height of the water above the bottom of the cylinder and the height of the outlet above the bottom as well. Water is affected by gravity. You can determine the pressure of the water by a few simple calculations. Do you know what the term 'head' means in fluid statics?

Rather than using Bernoulli's equation, how about Toricelli's Law:

http://en.wikipedia.org/wiki/Torricelli's_law

4. Jan 8, 2014

### slasakai

not sure how, as the pressure at the top of the cylinder is not given and the you can't use the equation P=P0+ρgh as the liquid is flowing

5. Jan 8, 2014

### SteamKing

Staff Emeritus
To get this cart moving, assume that the top of the cylinder is vented to atmosphere.

6. Jan 8, 2014

### slasakai

ok, so using Toricelli's Law you can get mass flow rate, and therefore the momentum of the water coming out of the valve, and therefore the force needed to keep it still. Thank you for your help!